The decision comes as RBS – which also sells mortgages under brands such as First Active and NatWest – bids for differentiation of its products in a market dominated by rival HBOS.
Neither RBS, Freuds nor Lansons would comment on the agency switch.
Lansons has had previous experience of working with RBS Group, promoting its credit cards between 2003 and 2005.
The One Account pioneered 'offset mortgages' in 1997. They work by effectively grouping customers' accounts, so cash left in their mortgage account at the end of the month is used for greater repayments.